The First-order Stochastic Dominance constraint mitigates the label switching problem [1]} of order-invariant latent states (see appendix fig:dirlabelswitching). Previous work has shown that the parameters of Hidden Markov Models (and admixture models [2]}) are identifiable up to permutation of the latent states [3]}. By definition, there exists a single ordering of random variables under the FSD constraint [4]}. In turn, the FSD-bounded rows of the OMD have a unique ordering.
